RP538 THE VAPOR PRESSURE OF LIQUID AND SOLID CARBON DIOXIDE By C. H. Meyers and M. S. Van Dusen ABSTRACT The vapor pressure of liquid carbon dioxide from the critical point (31.0° C.) to the triple point ( — 56.60° C.) and the vapor pressure of the solid from the triple point to the normal sublimation point ( — 78.515° C.) have been measured with an accuracy of 1 or 2 parts in 10,000. Equations have been obtained to represent these data, the average deviations from the equations being 1 part in 10,000 for the liquid and about 2 parts in 10,000 for the solid. The equation for the solid represents also the best work of other laboratories at and below —78° C. The vapor-pressure equation for the solid has been correlated with calorimetric data from other laboratories. Pressures and relative volumes have been observed along several isotherms in the critical region. A set of tables of the vapor pressure and the rate of change of vapor pressure with temperature calculated from the equations are given. CONTENTS Page I. Introduction 38 1 II. Preparation of samples 382 III. Description of apparatus and method 383 IV. Results of vapor-pressure measurements 385 V. Observations at the triple point 388 VI. Observations at the critical point 389 VII. Measurements by other observers 392 1. Observations at the triple point 392 2. Observations at the critical point 392 3 . Review of vapor-pressure measurements 394 VIII. Empirical representation of the data 399 1. Liquid carbon dioxide 399 2. Solid carbon dioxide 402 IX. Correlation of the vapor-pressure data with calorimetric data 404 X. Conclusions 407 XI. Acknowledgments 408 XII. Appendix 408 I. INTRODUCTION The determination of the vapor pressure is one of a series of investi- gations on the thermodynamic properties of refrigerants conducted at the Bureau of Standards. The measurements consisted of three sets made at different times. In 1919 and 1920 observations were made covering the range —55° to +31° C. The results of these observations were published 1 in 1926. These results have been recalculated and will be presented here together with the more recent observations. Ref. Eng., vol. 13, p. 180, 1926. 381
Transcript
RP538
THE VAPOR PRESSURE OF LIQUID AND SOLID CARBONDIOXIDE
By C. H. Meyers and M. S. Van Dusen
ABSTRACT
The vapor pressure of liquid carbon dioxide from the critical point (31.0° C.)
to the triple point (— 56.60° C.) and the vapor pressure of the solid from thetriple point to the normal sublimation point (— 78.515° C.) have been measuredwith an accuracy of 1 or 2 parts in 10,000. Equations have been obtained torepresent these data, the average deviations from the equations being 1 part in
10,000 for the liquid and about 2 parts in 10,000 for the solid. The equation for
the solid represents also the best work of other laboratories at and below —78° C.The vapor-pressure equation for the solid has been correlated with calorimetric
data from other laboratories.
Pressures and relative volumes have been observed along several isotherms in
the critical region.A set of tables of the vapor pressure and the rate of change of vapor pressure
with temperature calculated from the equations are given.
CONTENTSPage
I. Introduction 38
1
II. Preparation of samples 382III. Description of apparatus and method 383IV. Results of vapor-pressure measurements 385V. Observations at the triple point 388VI. Observations at the critical point 389VII. Measurements by other observers 392
1. Observations at the triple point 3922. Observations at the critical point 3923
.
Review of vapor-pressure measurements 394VIII. Empirical representation of the data 399
IX. Correlation of the vapor-pressure data with calorimetric data 404X. Conclusions 407XI. Acknowledgments 408XII. Appendix 408
I. INTRODUCTION
The determination of the vapor pressure is one of a series of investi-
gations on the thermodynamic properties of refrigerants conducted atthe Bureau of Standards.The measurements consisted of three sets made at different times.
In 1919 and 1920 observations were made covering the range —55°to +31° C. The results of these observations were published 1 in
1926. These results have been recalculated and will be presentedhere together with the more recent observations.
Ref. Eng., vol. 13, p. 180, 1926.
381
382 Bureau of Standards Journal of Research [Vol. 10
In 1927 one of the original samples of C02 (used in the first series)
was sent to the Massachusetts Institute of Technology where its
vapor pressure at 0° C. was measured. In 1929 the vapor pressureof the same sample at 0° C. and at 25° C. was measured at thisbureau.
In 1931 the vapor pressure of another of the original samples wasmeasured in the range —50° to —79° C. No measurements below— 79° C. have been made in the course of the work, but the publisheddata have been reviewed critically and used in deriving an empiricalequation for the vapor pressure of the solid over a wide temperaturerange.
II. PREPARATION OF SAMPLES
The liquid carbon dioxide used in these measurements was pre-pared by C. S. Taylor, formerly of the chemistry division of this
bureau. Sodium bicarbonate and concentrated sulphuric acid which
Figure 1.
—
Apparatus for preparing samples
had been heated in order to expel traces of air were used for this
purpose. The generating apparatus was very similar to that usedand described by Bradley and Hale.- The flask A (fig. 1) was abouthalf filled with sodium bicarbonate and sufficient distilled water wasthen added to form a thin paste. A dropping funnel B with its tip
turned upward and a gas delivery tube were introduced through a
rubber stopper which sealed the flask. The dropping funnel con-tained concentrated sulphuric acid, freshly boiled and cooled. Thedelivery tube was connected with the condenser C, traps, and dryingtrain.
The entire apparatus was evacuated to the vapor pressure of water,
the flask was heated to approximately 100° C. by means of a waterbath, and sulphuric acid admitted slowly into the flask. The flask
and line were purged by discharging some carbon dioxide through the
mercury seals F and G of traps D and E. Condensed water was also
discharged through these mercury seals. After the entire system hadbeen purged several times, the gas was allowed to flow through a
J J. Am. Chem. Soc, vol. 30, 1090, 1908.
vanDusen] Vapor Pressure of Carbon Dioxide 383
drying train containing CaCl2 and sublimed P2 5 , and finally frozen
into bulb N by cooling with liquid air. When sufficient quantity of
carbon dioxide had been collected in N, stopcock K was closed andthe bulb connected to the vacuum pump, so that any gas not occludedin the crystals would be pumped out. The liquid air bath was thentransferred to container and after bulb N had warmed sufficiently
so that gas was escaping freely through the mercury at L, the carbondioxide was sublimed into container 0. Gas not occluded in the
crystals was then pumped out as before. The carbon dioxide wasthen distilled into a glass high-pressure container M fitted with a
steel valve fastened to the glass by a method described elsewhere. 3
After the carbon dioxide had warmed up and liquefied, the valvewas opened slightly and the gas allowed to escape so rapidly that the
remaining liquid was frozen by its own evaporation. The valve wasthen closed until liquid formed and the process repeated several times.
The carbon dioxide was next sublimed into bulb P, the first and last
portions being rejected. Then, as before, any gas not occluded in
the crystals was pumped out. The carbon dioxide was sublimed backand forth between and P eight times in all, and then sublimed into
the apparatus sealed on at Q. While Q was still cooled with liquid
air the vacuum pump was connected to it, and the apparatus sealed
off at R by fusion.
As a test for purity 1,000 ml of the purified gas was dissolved in
potassium-hydroxide solution in a pipette. From the fact that theresidual bubble was microscopic and also from observations of thepressure when the sample was at liquid air temperature, togetherwith a knowledge of the capacity of the sample container, it was esti-
mated that the carbon dioxide contained less than 1 part in 1,000,000
i
by volume of noncondensing impurities.
III. DESCRIPTION OF APPARATUS AND METHODThe samples used in this investigation were contained in three
types of containers illustrated in Figure 2. Each of the containers of
type 1 consisted of a glass U tube about 2.5 mm inside diameter, to
which a valve was soldered. 4 These samples of carbon dioxide could
j
be totally immersed in the constant temperature bath. Of the two|
such containers filled in 1919, one sample (designated by No. 1) is
still intact (1932), the other (No. 2) failed by leakage through a sol-
dered joint after one day of observations.One container of type 3 was used. It consists of a glass bulb con-
! nected through glass tubing to a manometer (about 8 mm inside
|diameter and 1 m long) which was similarly soldered to a valve.
. During the observations the pressure was transmitted from the ma-nometer on the container of this sample to the pressure gauge by an
, air pressure approximately equal to the carbon dioxide pressure. ForI the observations made in 1931 the constancy of this transmitting
j
pressure was improved by attaching a container of about 1 liter capac-' ity to the line and immersing the container in an ice bath. In order\ to avoid pressures which might rupture the glass when the sample
'McKelvy and Taylor, J. Am. Chem. Soc, vol. 42, p. 1364, 1920. Meyers, J. Am. Chem. Soe., vol.45, p. 2135, 1923.
4 See footnote 3.
156547—33 7
384 Bureau of Standards Journal of Research [Vol. 10
was at room temperature, the amount of carbon dioxide used wassufficient only to produce liquid at temperatures below — 20° C.The containers of type A were of steel tinned inside and out.The pressures were measured with dead-weight pressure gauges
which are sensitive to better than 1 part in 10,000. These gauges,together with the calibration and method of use have been describedin a previous paper. 5
TO VALVE
TYPE 1
Figure 2.
TYPE 3
Containers for samples
Temperatures were observed with platinum-resistance thermom-eters of the 4-lead potential terminal type, with strain-free windingsinclosed in a tube.
The Wheatstone bridges used both in the earlier observations 7
and in those 8 of 1931 have also been described in previous papers.During the vapor-pressure measurements the carbon dioxide was
maintained at a constant and uniform temperature in one of a numberof stirred thermoregulated baths, the one chosen being determinedby the temperature and the type of carbon-dioxide container. Duringthe earlier observations the thermometer inserted near the carbondioxide sample indicated no changes greater than 0.005° C. for periodsof 20 minutes to 2 hours before the observation. The temperaturedifferences between various parts of the baths were of the same orderof magnitude. Some of the observations at 0° C. were made withthe sample in an ice bath. The observations in 1931 were made witha bath 9 which could be controlled for a long time within 0.001° or0.002° C. and which showed equally uniform temperature from place
to place in the bath.
» B. s. Jour. Research, vol. 6 (it. P. 32-1), p. 1061, 1081.
B. 8. Bull., vol. 6 (SUM), p, 1M. 1910. B. 8. Sol. Papers, vol. 17 (S407), p. 49, 1922.• B. s. Bull., vol. 11 (8341), p. 571, 1915.• B. 8. Bull., vol. 13 (S288), p. 547, 1917.• li. B. Jour. Research, vol. 6 (RP284), p. 401, 1931.
vanDmen] Vapor Pressure oj Carbon Dioxide 385
To obtain correct results with the static method used, it is necessarythat there be no temperature difference between the liquid or solid
surface of the sample and the thermometer, a condition which canoccur only when no condensation or evaporation is taking place. Inorder to reduce to a minimum the time required to attain such equilib-
rium within the sample, the apparatus was manipulated in such a waythat equilibrium was reached through condensation of a portion of
the sample. This precaution was found to be even more necessary for
the solid than for the liquid, since the solid sometimes broke loose
from the container and in consequence was in very poor thermalcontact with its surroundings. Attainment of equilibrium has beendiscussed in detail in connection with the vapor pressure measure-ments of ammonia. 10
IV. RESULTS OF VAPOR-PRESSURE MEASUREMENTS
The results of the observations on the vapor pressure of liquid
carbon dioxide are given in Table 1 . All the pressure measurementshave been reduced to millimeters of mercury at 0° C. and at standardgravity (g = 980.665). The value of g (980.091) assumed for this
laboratory is based on a determination made by the United StatesCoast and Geodetic Survey in 1910. 11 The thermometers have beencalibrated in accordance with the specifications for the internationaltemperature scale.
12
The results obtained with samples in metal containers (Type A)and previously published 13 were given no weight in selecting thefinal values and have been omitted, because the conditions of obser-vation were not conducive to accurate results, namely, (1) leaks in
the valve packings were found at numerous times, and small leakssufficient to lower the observed vapor pressure probably occurredundetected at other times; (2) the carbon dioxide may have acquiredimpurities in the connection between the metal container and the
;
pressure gage, such as air not completely washed out of the tubing!or wax dissolved from the valve packings.In numerous cases the previously published data represented the
' mean of several readings which may be considered as separate obser-vations, even though made successively at the same temperature,
jsince for each reading the sample occupied a somewhat differen t
j
volume. The values of temperature and pressure for these separate
J
observations have been recalculated and are given in columns 3 and
j4, respectively. A general increase of about 1 part in 5,000 over the
* previously published values of pressure is thus obtained.Not all the measurements recorded can be considered as having the
I same weight. In some cases the greater number of readings and longer
j
period of time covered insured that there was no drift in the observed
;values, and on some days the thermostat in the bath was operating
j
better than on other days. Lack of space prevents the presentation
jof all these details for the reader's judgment in the matter, but in the
ireview of the data an estimate was attempted of the relative merits
w B. S. Bull., vol. 16 (S369), p. 1, 1920. Am. Soc. Ref. Eng. J., vol. 6, p. 307, 1920.» B. S. Bull., vol. 8 (S171), p. 363, 1911." B. S. Jour. Research, vol 1 (R. P. 22), p. 635, 1928 .
» See footnote 1, p. 381.
386 Bureau of Standards Journal of Research [Vol. 10
of the observations. This estimate is recorded in column 5 of Table1 where the number indicates the weight to be given to the observationwhen an average value is to be taken. It is believed that the valuesthus weighted yield slightly more probable averages than would beobtained from equally weighted observations. The values calculatedfrom an equation (column 6, discussed in Sec. VIII of this paper)were not considered in making this estimate.The measurements in July, 1920, were made with special attention
toward securing thermal equilibrium, the bath temperature beingmaintained constant within 0.005° C. for two or three hours at eachof the temperatures 20°, 25°, 30°, and 31° C. Observations were madeat —5° C. during the same month, but the pressure readings wereerratic due evidently to partial freezing of the oil in the manometer.The trouble was so apparent that the data have been omitted. It is
possible that the observation taken at 0° C. during the same monthmay also be slightly in error due to the same cause. This source of
error has been avoided in all later measurements by substituting anoil with a lower pour point.
The accuracy of the observations taken in 1929 at 25° C. is impairedby a tendency of the bath temperature to drift. Although the tem-perature was kept constant within 0.005° C. by manual correction of
this tendency, the observations should be given less weight than otherobservations.The temperature of the bath used in 1931 for the range —50° to
-79° C. was remarkably constant (0.001° or 0.002° C), but theaccuracy of the observations in March of that year was limited byuncertainty in observing the mercury surface in a manometer attachedto the piston gage. The observations in April are more reliable, since
they were made after removing the mercury from the manometer in
question and allowing the transmitting air pressure to come directly
in contact with the oil in the manometer. In addition, more care wastaken to insure attainment of equilibrium.
Table 1.
—
Measurements of the vapor pressure of liquid carbon dioxide
388 Bureau oj Standards Journal of Research [Vol. 10
All observations on the vapor pressure of the solid were made in
1931 on the one sample in a container of type 3. (Fig. 2.) The pre-
vious remarks in regard to the weighting and accuracy of observationson the liquid are applicable also to the solid. The results of theseobservations are given in Table 2 which is similar to Table 1.
Table 2.
—
Measurements of the vapor pressure of solid carbon dioxide
1 This observation was made with the pressure gage disconnected and is therefore free from possible errorsarising in the use of the piston gage, including the one mentioned in the following note.
2 After the reading at —77.8 a leak from the container which held the transmitting air pressure was found.This observation is probably in error due to such leakage and no weight has been given to the result.
3 This value was obtained with a 100-bar gage, the value immediately above was obtained with a 10-bargage, the two gages being connected in parallel.
Note.—The uncertainty in reading the manometer on the sample container amounts to about 0.1 mm,but in some cases the values have been carried out to hundredths of a millimeter for purposes of comparison.
V. OBSERVATIONS AT THE TRIPLE POINT
All observations at the triple point were made on the one sample in
the container of type 3. For the observations in 1920 of the pressureat the triple point, a glass tube about 7 cm in diameter closed at thelower end was partially immersed in a constant temperature bath at— 52° C. The sample was lowered into the air space within this tubeand sufficient carbon dioxide snow to freeze a portion of the samplewas dropped into the tube. The liquid bath used in 1931 was undersuch excellent control that the sample was immersed directly in the
bath. For the observations of April 7 the bath was adjusted to
within a few hundredths of a degree of the triple point and observations
Meyers 1
Van Dusen] Vapor Pressure of Carbon Dioxide 389
taken continuously over a period of 1 hour and 40 minutes. Duringthis period there was a gradual rise in pressure within the limits givenin Table 3, which contains the observations of the triple point pressure.
This rise in pressure may be attributed to one or both of two possible
causes, namely (1) a small amount of impurity in the sample, and (2)
the solid may have been entirely covered by a film of liquid in whichtemperature gradients would be caused by heat transfer to or from thesample. In such case the vapor pressure would correspond to thetemperature of the liquid-vapor surface and the rise in pressure wouldbe explained by assuming that the temperature of this surface increasedabout 0.004° C. in consequence of the fact that the observer increasedthe bath temperature about 0.04° C. during the observations. If thevariation in pressure is caused by soluble impurities, the larger valueof pressure would be more nearly correct; if caused by variable tem-perature gradients, the smaller value would be more nearly correct.
The weighted mean of the values given in Table 3 is 3,885.27 mm.The vapor pressure equations for the liquid and for the solid, equations
(6) and (9), respectively, in section VIII of this paper, intersect at
about 3,885.10 mm and —56.602° C. These data indicate with fair
certainty that the triple point pressure and temperature are, respec-
tively, 3,885.2 ±0.4 mm and - 56.602 ± 0.005° C.
Table 3.
—
Measurements of -pressure at the triple point
Observed pressure
Weight ofDate
lOO-bargage
10-bargage
observa-tion
mm[ 3,884.11 3, 886. 9
1 3, 885. 4
I 3,886.1
J 3,885.05\ 3,885.20
/ 3,884.68\ 3,885.25
mm1
1June 3, 1920
1
Apr. 6, 19313, 885. 093, 885. 33
3, 884. 77
3, 885. 22
2
Apr. 7, 1931
2
2
2
Note.—The uncertainty in reading the manometer on the sample container amounts to about 0.1 mm,but in some cases the values have been carried to hundredths of a millimeter for purposes of comparison.
VI. OBSERVATIONS AT THE CRITICAL POINT
Visual observations of the phenomena taking place in the sample at
or near the critical point were made, but the critical temperature couldnot be fixed by this method much closer than about 0.1° C.
It may be noted that the critical point of a fluid is not a sharplydefined point, such as the triple point, and can not be determined withthe same degree of precision. No directly observable physical prop-erty exhibits a discontinuity at the critical point. The only discon-
tinuities are those in the derivatives of certain quantities with respect
to temperature or pressure, but such derivatives can not be directly
observed. The exact critical temperature is therefore subject toconsiderable uncertainty, but the pressure-temperature relation in
this region is definitely determinable. Near the critical point thecompressibility of a fluid is very great, and appreciable differences in
density therefore exist in a vertical column of the fluid. In this
390 Bureau of Standards Journal of Research \voi. 10
manner the action of gravity affects the observed phenomena, and thevalue chosen for the critical temperature will depend to some extentupon the interpretation of the observations.When the bath containing the sample was warmed at the rate of
about 0.002° C. per minute the meniscus gradually became fainter,
and finally changed to a band about 1 or 2 mm wide which disappearedat 31.06° C. When the bath was cooled at the rate of about 0.006°
per minute the band appeared at 31.02° C. When viewed withreflected light a gray fog was visible in the band, and through thetemperature range 31.05° to 31.15° C. this fog was faintly visible
throughout the sample.In addition to these observations of the meniscus or band, the rela-
tive volumes occupied by samples Nos. 1 and 2 at various pressureswere measured along several isotherms in the critical region. Forthese observations the sample was immersed in a bath maintainedwithin a few thousandths of a degree centigrade of the constant temper-ature desired. The carbon dioxide was first expanded until it
existed as a superheated vapor. Then the weight on the piston gagewas increased by small increments. After time had been allowedfor attainment of equilibrium subsequent to each increase in weight,the pressure and the length of the carbon dioxide column were ob-served. At some of the temperatures the length of tube occupiedby the carbon dioxide was also observed at the beginning and at theend of condensation.The diameter of the tube was assumed constant except for the end
which had been tapered in the sealing off process. This tapered endwas assumed to be a cone and one-third of its length was added to thelength of the portion of uniform diameter. The observed lengths of
sample No. 2 had to be multiplied by the factor 1.075 to make themcomparable with those of No. 1. Since the uncorrected length wasusually measured with an accuracy of not better than one-half milli-
meter, errors of 1 or 2 per cent in the measurement of relative volumemay be expected.
These measurements are represented in Figure 3 where the pressureis plotted as ordinate and the corrected length of tube as abscissa.
It is apparent that the shape of the isotherms can not be used as a
criterion for determining the critical temperature within 0.2° or0.3° C.
It was at first thought that since the temperature of disappearanceof the band depended to some extent upon the illumination, the meanof the temperatures for disappearance and appearance of the band,31.04° C, was at or slightly below the critical temperature. Theobservations of Kennedy and Meyers 14 on the same sample in whichthe meniscus was observed to be a sharply defined surface up to about30.96° C. and to be a band of finite width above this temperature, as
well as their observations on samples in capillary tubes, and further
consideration of the matter leads to the belief that the critical tem-perature is very near 30.96° C.
It is believed that the band observed above this temperature is
due to the rapid change of density and optical properties with pres-
sure for the single phase which is enormously compressible in the
>< Ref. Eng., vol 15, p. 125, 1928.
Meyers]
Van Dusen] Vapor Pressure of Carbon Dioxide 391
critical region, and that this band would not be present if the samplewere not in a gravitational field. Probably even a few hundredthsof a degree below the critical temperature, the density of both theliquid and vapor at an infinitesimal distance from the meniscusdiffers appreciably from that in the remainder of the sample.
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Figure 3.
—
Isothermals for carbon dioxide in the critical region
O represents data on sample No. 1. • represents data on sample No. 2. X point at which thecarbon dioxide surface or band was either at the top or the bottom of the space. < > on theisotherm at 31.08° C. indicate that at volumes between these marks, fog was observed through-out the sample, while it could not be seen when the volume was outside these limits.
If this belief is correct the upper dotted curve in Figure 3 is not thetrue saturation curve, even though it was drawn approximatelythrough the crosses which represent the average relative volume forthe whole sample when the meniscus or band was either at the bot-tom or the top of the space occupied, but the lower dotted curverepresents more nearly the state of the two phases under saturationconditions; that is, at the meniscus.
392 Bureau of Standards Journal of Research [Vol. 10
VII. MEASUREMENTS BY OTHER OBSERVERS
Measurements of vapor pressure by various observers are compar-able only when both pressures and temperatures are expressed in
units reducible to a common basis.
The pressure measurements quoted for comparison in the presentpaper were stated in units reducible to bars through multiplication bya constant factor.
Temperatures are given as reported by the authors, no attemptbeing made to take account of possible differences in temperaturescales. With the exception of some data at the triple point, all tem-peratures tabulated in this paper differ from the international tem-perature scale by an amount less than the experimental error.
1. OBSERVATIONS AT THE TRIPLE POINT
The measurements of the triple point pressure, with the exceptionof those made by Faraday, who consistently observed high pressures
for carbon dioxide, are practically in agreement with the presentwork. The observed temperatures are in agreement as well as canbe expected considering the instruments used by the various observers.
Table 4 shows the temperature and pressure observed at the triple
point, the name of the author, and the reference to the publication.
The results of this investigation are included for comparison.
Table 4.
—
Data of various observers on carbon dioxide at the triple point
Observer and reference
Faraday, Trans. Roy. Soc, London, p. 155, 1845.
Villard and Jarry, Compt. rend., vol. 120, p. 1413, 1895.
Kuenen and Robson: Phil. Mag. (6) vol. 3, p. 149, 1902.
Zeleny and Smith, Phys. Rev., vol. 24, p. 42, 1907; Phys. Zs., vol. 7, p. 667, 1906.
Values from the present investigation.
2. OBSERVATIONS AT THE CRITICAL POINT
Table 5 gives a comparison with the present data of the results of
various observers for carbon dioxide at the critical state.
Verschaffelt (1896) observed the capillary rise of the carbon dioxide
in a glass tube a few tenths millimeter in diameter, at various tem-peratures up to 30° C. and extrapolated the data to a temperature at
which the rise was zero. This he interpreted as the critical tem-perature.
Kuenen (1897) and Keesom (1903) observed the temperature at
which the meniscus disappeared, and interpreted this as the critical
temperature.Von Wesendonck (1903) found that by repeated inversion of the
vertical containing tube, a uniformly distributed fog was formed in
the carbon dioxide in the temperature range 30.95° to 31.7° C.
This fog remained indefinitely. Above 31.7° C. it decreased until
at 32° C. it had entirely vanished.Onnes and Fabius (1907) reported the critical temperature of
carbon dioxide to be 30.985° C. The disappearance or the appear-
ance of the meniscus with slow heating or cooling occurred at tem-peratures which differed by only 0.02° C. The carbon dioxide usedby them was first purified until the molecular proportion of impuri-ties was estimated to be less than 3 parts in 10,000, after which it
was fractionally distilled and sublimed.Bradley, Browne, and Hale (1908) used the method of preparing
carbon dioxide which was followed in preparing material for thepresent investigation, with the exception that they used sulphuricacid in the first drier and did not sublime the carbon dioxide. Theyobtained material which contained 1 part in 30,000 or 40,000 of gases
not absorbed in potassium hydroxide solution. They give the critical
temperature as 31.26° C, the mean of the two temperatures at whichthe meniscus disappeared or appeared differing by 0.08° C.
Cardoso and Bell observed the critical temperature and pressure of
two samples of carbon dioxide which had been purified first by passingthrough five flasks of sulphuric acid and a long tube of phosphoruspentoxide, and second by 10 sublimations. The critical constants for
one sample were found to be 31.00° C. and 72.77 atmospheres, for theother 31.00° C. and 72.90 atmospheres. They used a closed endnitrogen manometer and a calibrated mercury-in-glass thermometer.They estimated the accuracy of their results as 0.1° C. and 0.1
atmosphere.
Table 5.
—
Data of various observers on carbon 4ioxide at the critical point
Observer and reference
°C.30.92
3131.931.3531.40
31.731.031.131.4
30.95to
31.730.9831.1230. 985
31.26
31.1031.0030.9730.96
atmos-pheres73
7772.9
73.26
72.93
73.0072.85
Andrews, Trans. Roy. Soc. London, vol. 159, II, p. 575, 1869.
Hautefeuille and Cailletet, Compt. rend., vol. 92, p. 840, 1881.
Dewar, Phil. Mag., vol. 18, p. 210, 1884.
Amagat, Compt. rend., vol. 114, p. 1093, 1322, 1892.Chappuis, Compt. rend., vol. 118, p. 976, 1894.
Onnes and Fabius, Versl. Kon. Akad. Amst., p. 44, 1907; Proc. Kon. Akad. Amst.,vol. 10i, p. 215, 1907-8; Comm. Leiden No. 98, 1907.
Bradley, Browne, and Hale, Phys. Rev., vol. 26, p. 470, 1908.
Dorsman, Dorsman Diss. Amst., 1908.
Cordoso and Bell, J. chim. phys., vol. 10, p. 500, 1912.
Hein, Zs. physik. chem., vol. 86, p. 385, 1913-14.
Kennedy and Meyers, Ref. Eng., vol. 15, p. 125, 1928.
Hein used the same method of preparing the carbon dioxide as
Bradley, Browne, and Hale, but used apparatus entirely of glass,
the only ground joint being in the stopcock in the dropping funnel.
He estimated that the carbon dioxide contained not more than 1
part in 30,000 of air or other gas. The vapor of boiling propylchloridewas used to maintain constant temperatures; and a calibrated ther-
mometer divided in 0.1° C was used to measure temperatures.The more accurate of the observations in Figure 5 indicate that
the critical temperature is between 30.95° and 31.05° C. For prac-
394 Bureau of Standards Journal of Research [Vol. 10
tical purposes it probably will be sufficient to use 31.0° C. for whichthe corresponding calculated pressure (equation (6), Sec. VIII of this
paper) is 72.80 atmospheres or 73.76 bars.
3. REVIEW OF VAPOR PRESSURE MEASUREMENTS
Onnes and Weber 15 measured the vapor pressure of the solid in
the temperature range — 183° to — 135° C. A form of Knudsen'sabsolute manometer was used for the lower pressures.
A hot wire manometer which had a greater sensitivity than theKnudsen manometer was used for the higher pressures.
Their data on vapor pressure are precise to about 5 per cent or
better at the lower temperatures and to a few tenths of a per centat the higher temperatures.The fact that their values at liquid air temperatures appear to be
too high indicates that the samples contained traces of noncondensingimpurities too small to be appreciable at the higher temperatures.This is confirmed by the fact that after the sample had warmed upand stood for a few days, the residual pressure at — 200° C. increasedfrom 0.007 to 0.016 microbars. A second series of measurementswas corrected for this increase to make it comparable with the first.
Since boiling liquid baths of ethylene, methane, and oxygen wereused, it is to be expected that the observed vapor pressure wouldbe low because the thermometer can not be placed near the coldest
part of the sample; that is, at the surface of the bath. In fact suchis the case at the upper end of the temperature range where themeasured pressure is relatively large (1,400 microbars), the observedvalues being about 1 per cent lower than the values calculated fromequation (9), Section VIII of this paper, which are in agreement withcalorimetric data and with vapor pressure measurements at highertemperatures. This discrepancy corresponds to about 0.07° C.The thermal molecular pressure correction discussed in detail by
Knudsen 16 becomes appreciable at temperatures below — 140° C,and in the range —150° to —165° C. is uncertain.Siemens 17 measured temperatures in the range —128° to —77° C.
with a platinum resistance thermometer. The sample was in a con-tainer somewhat similar to the container (type 3) Figure 2 exceptthat one side of the manometer was evacuated. The inside diameterof the manometer was 10 mm. The apparatus was evacuated througha side tube and carbon dioxide, generated from sodium bicarbonateand sulphuric acid, admitted to the apparatus. The carbon dioxide
was purified by at least three sublimations. After each sublimationgaseous impurities were pumped out while the carbon dioxide was at
liquid air temperature.For the observations at temperatures within a few degrees of the
normal sublimation point, the sample was placed in a bath whichconsisted of a thin mixture of carbon dioxide snow and alcohol rapidly
stirred by a propeller. Air was admitted to the top of the bath so thatthe temperature was lowered below the sublimation point. Before areading was to be taken the stirrer was stopped, thus allowing the solid
» Comm. Phys. Lab. Univ. Leiden Nos. 137b and 137c, 1913; Proc. K. Akad. Wetensch. Amst., vol.16i, pp. 215 and 445, 1913.
»« Ann. Pbysik (4), vol. 31, pp. 205 and 633, 1910, and (4), vol. 33, p. 1435, 1910.« Ann. Physik (4), vol. 42, p. 871, 1913.
vanDusen] Vapor Pressure oj Carbon Dioxide 395
to settle with a consequent reduction in the evaporation and an in-
crease in the temperature of the bath. Siemens believed that this
expedient produced a bath warmer at the top. Although thermalconduction down the walls would tend to warm the bath from thetop, yet the presence of air would accelerate the evaporation of carbondioxide from solution, and it is a debatable question whether the sur-
face of the bath was actually warmer than the remainder of the bath.
Even if the attempt to make the top of the bath the warmest portion
were successful, the temperature of the sample which is probably in
poor thermal contact with the bath would lag considerably behindthe rising bath temperature with consequent low observed pressures.
The question of lag has been discussed in Section III of this paper.
For lower temperatures a large copper block was hung over liquid air
in a Dewar flask. This block contained two wells filled with alcohol
or pentane, in which the thermometer and the tube containing thesample of carbon dioxide were immersed. The sides and upper sur-
face of this block were packed with insulating material. The tem-perature was controlled by raising or lowering the vessel containingthe liquid air. Better observations are to be expected with this baththan with the former.Henning 18 at the Physikalisch Technische Reichsanstalt measured
the vapor pressure in the temperature range —81° to —78° C. Forthis purpose he used a bath 19 of petroleum ether in a silvered Dewarflask. The bath was cooled by a regulated stream of liquid air whichwas delivered to one side of a U tube, and, after evaporation, wasexpelled from the other side. This U tube, together with a screwpropeller, was inclosed in a porcelain tube which had holes in its side
at several different heights. The petroleum ether was drawn into
the botton of the porcelain tube and forced past the U tube and outthrough the holes in the side of the porcelain tube. With only oneexception the readings of the two platinum resistance thermometersused in the bath agreed within two or three hundredths degree.
The sample of carbon dioxide was contained in a glass apparatusonly slightly different from that used by Siemens, the two arms of themanometer being separated and their open lower ends immersed in adish of mercury. The manometer was read with a cathetometerreadable to 0.01 mm. The sample of carbon dioxide was preparedby heating sodium bicarbonate and purified by numerous sublima-tions under reduced pressure.
Henning and Stock 20 measured the vapor pressure of carbon dioxidein the temperature range — 110° to —80° C, with the aid of the samedesign of bath previously used by Henning. The thermometer of
pure platinum used for these measurements had been carefully cali-
brated by comparison with a gas thermometer. The value given for
the normal sublimation point is —78.52° C. The samples of carbondioxide were obtained both from commercial tanks and by the heatingof sodium bicarbonate previously evacuated. The samples from eachsource were purified by alternately subhming in liquid air and pump-ing off noncondensing gases with a vacuum pump three times for thefirst source and one for the second.
» Ann. d. Phys. (4), vol. 43, p. 282, 1914.» Zeits. fur Inst., vol. 33, p. 33, 1913." Zeits. fur Phys., vol. 4, p. 226, 1921.
396 Bureau of Standards Journal of Research [Vol. w
The measurements at the Reichsanstalt were repeated by Heuseand Otto 21 in connection with a comparison between the internationaland the thermodynamic temperature scales. For the measurementsat the normal sublimation point of carbon dioxide they used the sameconstant temperature bath previously used by Henning. The vaporpressure thermometer was improved over previous designs by theinclosure of the stem in a vaccuum jacket which extended from theportion at room temperature to near the end of the portion immersedin the bath. A bulb of about 1 cm 3 was left exposed to the bath.This insured that the bulb contained the coldest part of the sample,and consequently its temperature would correspond to the pressuremeasured. Two platinum resistance thermometers of the strain-free
type were used as well as a hehum gas thermometer which could at
the normal sublimation point of carbon dixide be used either as aconstant volume or constant pressure thermometer. The manometerwas supplied with one fixed platinum point on the side connected to
the gas thermometer and a series of fixed points on the other side sothat the mercury could be adjusted on both sides of the manometerto optical contact with a pair of fixed points whose vertical distancehad been measured. Their first series of measurements indicatedthe temperature of the normal sublimation point to be —78.483° and-78.523°, while the second seriesgave -78.471° and -78.509° C,respectively, on the thermodynamic and international scales.
Bridgeman - measured the vapor pressure of carbon dioxide at0° C. Four piston gages were specially calibrated with an 8 m mer-cury column for this purpose. Groups of observations with these
gages differed by only 1 part in 10,000. The process of purification
is not described in detail, but the average difference observed for
two samples is only 1 part in 40,000. The value given as a final mean(26,144.7 ±1.0 mm) differs only about 1 part in 10,000 from the value(26,141.7 mm) calculated from equaton (6) and 2 parts in 10,000 fromthe mean of the observed values in this investigation.
Table 6 fists the vapor pressure observations which have been givenweight in obtaining an equation for representing the vapor pressure
as a function of temperature. The table gives also the correspondingvalues calculated from that equation, and the differences between the
observed and calculated values.
« Ann. Physik (ser. 5) vol. 9, p. 486, 1931; vol. 14, pp. 181 and 185, 1932." J. Am. Chem. Soc. vol. 49i, p. 1174, 1927.
References to papers not already discussed which contain data onthe vapor pressure of carbon dioxide are listed below.- 3 A few of thesecontain data on the solid, but have been given no weight in thedetermination of the constants in the empirical equation.Some of the more accurate measurements on the liquid are com-
pared with the results given in this paper in Figure 4. The dottedcurve indicates the percentage error corresponding to an error of0.5° C. The zero line has been drawn sufficiently wide to include all
the observations on samples is glass used in the present investigation.
The results of Jenkin and Fye shown in Figure 4 are unique in
being the only measurement of the vapor pressure of carbon dioxidebv the dynamic method.
List of references on the vapor pressure of carbon dioxide.
xaraday...
RegnaultAndrews
s
Pistol
Amagat
Villard and JarryYillardKuenen.duBois and WillsHolborn.Kuenen and KobsonLange -
Keesom
.I'liy
Nernst Falck).Jeukin and Pye
, wnshend and Young
Reference
Trans. Roy. Soc.. London, p. 155. 1845; Faraday's Researches in Chemistryand Physics (Univ. London Press. .-
Relation des Experiences, vol. 2. p. 518, 1S62 i,Mem. Acad. Sci. Paris, vol. 26).
Trans. Roy. Sob. London, vol. 159, II. p. 575. 1869; Scientific Papers of
Thomas Andrews (MacMfltan A Co. 1889).Phil. Mag. (6), vol. 1. p. 7S. 1S76: Ann. chim. ph; - p. 555. 1S76.
Arch. sci. phys. Nat Geneve, vol. 61. p. 91, 1S7S: Ann. chim. physvol. 13, p. 212. 1878.
Ann. chim. phys. (,6). vol. 29, p. 136. 1893; J. phys. (.3). vol. l. p. 288, 1893;Compt. rend., vol. 114. pp. 1093 and 1322. 1898.
Compt. rend., vol. 130, p. 1413. 1895.
Ann. chim. phys. C7), vol. 10, p. 3S7. 1887.
Phil. Mac. C6), vol. 44. p. 179. -
Yerh. d. Ges.. vol. l. p. 168, 1899.
Ann. Physik. vol. 6. p. 2o3. 1901.
Phil. Mag. (6), vol. 3. p. 149. 1902.
Z. ang. Chem.. vol. 16. p. 514. 1803.
Comm. Phys. Lab. Univ. Leiden No H Proc. Kon. Akad. Amst.,vol. 6. 11. p. 565, 1904.
Phys. Zts.. vol. 7. p. 716, 1908; Phys. Kev.. vol. 23, p. 308, 1900.
Phys. Zts., vol. 9. p. 435. 1903.
5. Roy. SOC. I«ondon, vol. 213. p. 67. 1913.
.ath. and Phys., vol. 1. p. 243. 23
MeyersVan Dusen Vapor Pressure of Carbon Dioxide 399
VIII. EMPIRICAL REPRESENTATION OF THE DATA
1. LIQUID CARBON DIOXIDE
For the representation of vapor pressure, an equation of the form
log£_^!o| A^vtz6o +CPo 6
A-B '(*?/ a)
has been used by Cragoe,24 where p and p are, respectively, theobserved pressure and the pressure at some standard temperatureand and 6 are the corresponding absolute temperatures. Inorder to represent the measurements of the vapor pressure of liquid
carbon dioxide within the limits of accuracy of the observations, it
was necessary to add two terms involving higher powers offl
- .,
' o 1 °,
»
[
*
»
!1 CI I
•I
ci . L 5
*1
•
"
1
!
..."...J
;
2»
> rJ— -
'
-----
i
•>
*
i
.
- s
Figure 4.
—
Comparison of the measurements on liquid by various observers
The dotted curve shows the deviation in per cent of the pressure corresponding to an error of 0.5° C. Thepoints shown are:
# Kuenen.3 Kuenen and Robson.C> Keesom.•- Zeleny and Smith.
O Jenkin and Pye.
With the addition of these two terms, the choice of d as 0° C, and analgebraic transformation, the equation
log p= 1.542235 (3.136105 f+0.000578554 t2
273.10+ *
+ 2.77120 f3 10" 5 + 3. 19406 t
4 10~ 7 + 3. 17316 f 10" 9) (2)
was obtained, t is the temperature in degrees centigrade on the inter-
national scale, and p is the pressure in bars.
f
Another equation has been obtained through graphical representa-tion of the data. The values of log p obtained from the observa-
u Int. Critical Tabl"?, vol. 3, p. 228, McGraw Hill Book Co.
17—a—
s
400 Bureau of Standards Journal of Research [Vol. 10
tions are approximately a linear function of temperature as may bededuced from the fact that the well-known equation
log p = a~ (3)
where a and b are constants, is a fair approximation. Consequently,(a — log p) has an almost constant value. This quantity was
plotted as ordinate with the square of the absolute temperature asabscissa. The points plotted lay on a curve which had a point ofinflection and a form approximately that of a cubic. When a valueof a was chosen such that the slope of the curve was zero at thepoint of inflection as in Figure 5, the curve was symmetrical about
-60 -40 -20 20 C1 1
'
[ 1 1
//
//
'
/75 80 8545 50 55 60 65 70
(ABSOLUTE TEMPERATURE)2X I0"
3
Figure 5.
—
Term subtracted from b in equation (6).
90 95
the point of inflection within the accuracy of the data. The positionof the point of inflection was determined with sufficient accuracyby plotting on separate large semitransparent sheets of paper thepoints on the opposite sides of the point of inflection and super-imposing the two parts of the curve thus formed.
It was found that the equation
d(a-\ogp) = b-c(62 -el
2)
[
(4)
vi here c is a constant and 0i is the temperature at the point of inflec-
tion, represented the data within about 1 part in 2,000, but that a
consistent deviation from the observed values still existed, the curve
vanDusm] Vapor Pressure of Carbon Dioxide 401
in Figure 5 being steeper at the extremities than would be indicated
by equation (4). This led to the use of the equation
d (a -log p) = b- my (10 ny2 -l) (5)
or
\ogl0p = a-}{b- my (I0 n*2
-1)} (6)
where for liquid carbon dioxide with p in bars
a = 4.6741936 = 855.352m = 1.131X10~4
™ = 4.7X10- 10
0!2 = 69,700 (0x = 264.01)
The term which has been added to equation (3) is relatively small
(0.3 per cent of b or less for liquid carbon dixoide), and the use of a
table of squares, a table of logarithms, and a slide rule yields valuesof this term with sufficient accuracy for calculating the vapor pressureof liquid carbon dioxide to 1 part in 10,000.
The pressures in the sixth column of Table 1 were calculated fromequation (6) using the values given for the constants. The differences
between observed and calculated pressures in millimeters, in parts in
100,000, and in thousandths of a degree centigrade are given, respec-
tively, in the last three columns of the table. There is no apparentconsistent variation in these differences with temperature. Thereproducibility of pressure measurements on a given day indicates
that an appreciable part of the differences for different days may bedue to small irregularities in the behavior of the Wheatstone bridgeused, especially for the measurements at the higher temperatures.
Differentiation of equation (6) gives
^-3^=|[6-m2/(10»"
2
-l)] + 2m[10»''J
(4.605 y+l)-l] (7)
The values of pressure and of dp/dB for liquid carbon dioxide givenin the appendix to this paper have been calculated from equations
(6) and (7), using the constants already given.
Figure 6 gives an intercomparison between values calculated fromequations (2) and (6), and groups of observed values. The upperpart of the figure shows deviations from equation (2) and the lowerpart shows deviations from equation (6). The cross represents themean of observations made on sample No. 1 at 0° C. at the Massa-chusetts Institute of Technology. The solid black circle at 0° C.represents the mean of the observations by Bridgeman. 25 The pointis shown in this figure since the accuracy of his results and the agree-ment with this investigation are better than can be indicated on themore compressed scale used for other observations in Figure 4. Theremaining circles represent observations made at this bureau. Thepoint at —55° C. which is omitted in the upper part of the figure,
represents only a single observation; its percentage deviation is rela-
Ji See footnote 22, p. 396.
402 Bureau of Standards Journal of Research [Vol.10
tively large, but corresponds to an error of only 0.011° C. in thetemperature. Each of the other circles represents the mean of sev-eral observations. The values for plotting these points were obtainedby dividing the values in the eighth column of Table 1 into groupscovering small temperature ranges and taking a mean of the valuesin each group, weighted as indicated in the fifth column of the table.The figure shows that both equations represent the data almostequally well, although near the critical temperature equation (6)appears to be slightly better. This equation probably represents thevapor pressure of the samples observed within 1 or 2 parts in 10,000.The values of dp/dd calculated from the two equations differ by less
than 1 part in 1,500 in the temperature range -56° to 25° C; but
1
'
2 }( )
!
V <
< 1
1 ( >
/-*r
o1
1
—
1
—"'"~s ' /fOUATrCN <:
< >o
(
—^_c < >
EQUATION 2<^ \ 8
/° 1 1
EGUATION S ;c~—" \
2\
4< >
!
DEGREES CENTIGRADE
Figure 6.
—
Intercomparison of equations (2) and (6) and observed values
X represents mean of observations at 0° C. on sample Xo. 1 by Massachusetts Institute ofTechnology. Q mean of observations at this bureau. Point at —55° C, is a single observationand is omiited in the upper part of the figure. # mean of measurements by O. C. Bridgeman
at 31° C, equation (6) yields the larger value by 0.5 per cent. Noexact estimate can be made of the accuracy of the values of dp/ddcalculated from equation (6), but it seems fairly certain that the ac-
curacy is better than 1 part in 1,000 except near the critical tempera-ture and that the error does not exceed 0.5 per cent at that point.
This accuracy is considered ample for use in the Clapeyron-Clausiusrelation
L/e = (V-v)dp/dd (8)
since the latent heat and difference between the specific volumes of
the vapor and liquid approach zero as a limit at the critical tem-perature.
2. SOLID CARBON DIOXIDE
Over the temperature range within which accurate vapor pressure
data have been obtained for solid carbon dioxide the results can berepresented in bars by the equation
O Weber, Leiden Comm. No. 137c, 1913 (lower chart).
O Onnes and Weber, Leiden Comm. No. 137b, 1913 (lower chart).X Heuse and Otto, Ann. Physik (ser. 6), vol. 9, p. 486, 1931, and vol. 14, pp. 181 and 185, 1932.
(see footnote to Table 2). The coordinates have been chosen to giveas nearly as possible a uniform dispersion of the points throughoutthe temperature range. The dotted lines indicate the errors in tem-perature corresponding to percentage errors in the pressure while thescale of pressures at the top makes possible an estimate of the absolutevalue of the pressure differences. These points form four groupscovering small temperature intervals in the temperature range —56.6°to —80° C. If the mean of the points in each group, weighted as
404 Bureau of Standards Journal of Research [Vol. 10
indicated in Table 2, is taken, the maximum deviation from the equa-tion for these means is 2 parts in 10,000.
It will be seen that these observed values and equation (9) are bothin excellent agreement with the work at the Reichsanstalt. There is
also good agreement at the lower temperatures with the observationsof Siemens, but his observations near the normal sublimation pointare so low as to be off the scale used in the figure. This discrepancyis discussed in part 3 of Section VII of this paper.The observations of Onnes and Weber are very precise except for
their value at — 129° C. which is far off the scale used. From Figure 7
alone, one might conclude that the equation did not actually representthe vapor pressure below —100° C, but it is shown in Section IX of
this paper that the equation is in much better agreement with pres-
sures calculated with the aid of calorimetric data than are the ob-served values.
200 TEMP.°K
3
150°
145 5t)
D14 t-
m<r
135 Ia
a
, '"F
"'
----"* —— .... l^i^^
. 'E Ac— " -" /
J
S\S e
s
130 <
Figure 8.
—
Correlation of vapor pressure data with latent heat of sublimation
AA, values of—- -£ from equation (9).
LL, same from equation given by Weber.BDE and BDF, possible values for latent heat of sublimation.
calculated latent heat from AA and volumetric measurements of Maass and Mennie.Observed latent heats are as follows:
Q Andrews, J. Am. Chem. Soc, vol. 47, p. 1597, 1925.
ft Favre, Compt. rend., vol. 39, p. 729, 1854; Liebig's Ann., vol. 92, p. 194, 1854.
(Other references given in the text.)
IX. CORRELATION OF THE VAPOR PRESSURE DATA WITHCALORIMETRIC DATA
It is desirable to correlate calorimetric data with the vapor pressure
and to use this correlation as an aid in estimating the accuracy of the
calculated values of the vapor pressure particularly at the lowertemperatures where the percentage accuracy of the vapor pressure
measurements is relatively poor.
From the exact Clapeyron-Clausius relation (see equation (8))Tin
and the approximation, V—v=— » which is sufficiently accurate at
the lower temperatures, one obtains
L = —dp/dd (10)
vanDusen] Vapor Pressure oj Carbon Dioxide 405
Rd2
Values of — dp/dd for the solid were calculated from equation (9),
plotted in Figure 8 as ordinates with temperature as abscissa, andrepresented by the curve AA.
Of the various observed values of latent heat represented in thefigure, the two by Eucken and Donath 26 are probably the mostaccurate. The agreement between the various data presented in thefigure confirms the claim of those authors for an accuracy of 0.1 or0.2 per cent. The point at — 133.1° C. coincides with the curve AA,while the point at — 103.1° C. is slightly below the curve AA in con-
sequence of the fact that V— v departs from— at the higher tempera-
tures. It is to be noted that the value for the latent heat at — 133.1°
C. published by Eucken and Donath is 0.2 per cent smaller than themean of their observed values which is given in Figure 8.
The square at —70° C. represents a value of latent heat calculatedfrom equation (8) using the value of dp/dd obtained in the presentinvestigation and an extrapolation to the saturation pressure of thevalue obtained by Maass and Mennie 27 for the specific volume of thevapor at about one atmosphere. This extrapolation was based on theassumption that at constant temperature PV varies linearly with thedensity.
The curve from B to D was drawn approximately through the threepoints under discussion. It is in agreement with the observation of
the latent heat at the normal sublimation point by Maass andBarnes,28 and except near the triple point, with the values chosen byPlank and KuprianofT 29 in their correlation of the properties of carbondioxide.
At temperatures lower than —133.1° C, the latent heat may becalculated from Eucken and Donath's observed value at that tempera-ture and an integration of specific heat data. For carbon dioxide at
these low temperatures the equation
Gttu-CtnUt = dLld9 (11)
is a very close approximation to the exact thermodynamic relation
Crtu -C
=
dL/de - L/e + {(]!),„.-(~yollA
]dP/de. (12)
For the purpose of this integration Eucken's 30 determinations of thespecific heat at constant pressure for the solid were used. In thetemperature range above — 170° C. these observations can be repre-
sented by the equation
^8oiid= 0-60+ 0.00330,j/g°C.
= 0.143 + 0.000790, cal/g°C, or Btu/lb°F. (13)
Below this temperature integration was performed by choosing from agraph, the average differences between the specific heat for the gasand for the solid over a limited temperature range and multiplying
" Z. phys. Chem., vol. 124, p. 181, 1926.« Proc. Roy. Soc., London, Ser. A. vol. 110, p. 198, 1926.2* Proc. Roy. Soc, London, Ser. A, vol. Ill, p. 224, 1926.*• Beiheft Z. ges. KSlte-Ind. Reihe 1, Heft 1, 1929.30Verhand, Deutschen phys. Gesell., vol. 18, p. 4, 1916.
406 Bureau of Standards Journal oj Research [Vol 10
by the temperature increment. Although the values of specific heatpublished by Maass and Barnes 31 differ somewhat from those byEucken, it appears that a correction should be applied to their dataespecially at the higher temperatures for evaporation of part of thesample when warmed, since the solid did not fill the container entirely.
Although the information available was insufficient for determiningthis correction accurately, it appears that the correction is of theproper magnitude to bring the two sets of data into substantialagreement.The specific heat of the vapor is not well established at low tem-
peratures by experimental values, the observed value at the lowesttemperature being 0.768 joules per gram per °C, at 1 atmosphere and-75° C. byHeuse.32
Theoretical considerations have led various authors to believe thatCp for carbon dioxide vapor approaches S.5R or 0.662 joules per gramper °C. as a limit at absolute zero. A graph of the available dataplotted with specific heat and temperature as coordinates indicates
that if this is the limit approached, CPgaB below — 130° C. may for our
purpose be considered equal to the limiting value. With this assump-tion
/is represented by the curve DE in Figure 8.
The graph of experimental data mentioned does not determine the
limiting value for Cp . If, as is believed for hydrogen, the limit is
2.5R, a smooth curve through the experimental data near saturation
and through 2.5R at absolute zero is, to a first approximation, repre-
sented by assuming CPgaB equal to 0.473 + 7.5 X ,1O~ 6,0
2. This assump-
tion leads to the curve DF in Figure 8.
An integration of the function represented by the curve DF gives
values for vapor pressure about 15, 3, and 0.3 per cent smaller at— 190°, —170°, and —150° C, respectively, than those obtainedfrom equation (9). The corresponding differences between values
obtained from integration of the function represented by DE andthose from equation (9) are about one-third as great. The curveBDE probably gives as good an estimate of the latent heat of sub-limation as can be made from the available data.
Weber and Onnes 33 have shown that their measurements in the
range — 180° to — 130° C. are very well represented by the equation
Values of—dp/dd calculated from this equation are represented by
the dotted curve LL. It is apparent that their observations are notin agreement with calorimetric data.
From this correlation of the data it appears that the vapor pressures
calculated from equation (9), although considerably smaller at verylow temperatures than the observed pressures, are not too small butmay be slightly too large.
»i See footnote 28, p. 405.' Ann. Physik (4), vol. 59. p. 86, 19 IP.
» See footnote 16, p. 394.
vannusen] Vapor Pressure of Carbon Dioxide 407
It is to be noted that under conditions such as occur in the presentcase where the percentage accuracy of the observed vapor pressures
decreases with decreasing temperature, the vapor pressure equation
gives the quantity -dp/dd with greater percentage accuracy than it
does the quantity dp/dd or even the vapor pressure itself. For ex-
ample, two equations which gave at — 130° C. the same vapor pres-
sures and the same values for JL-dp2/d6, yielded at —190° C. vapor
pressures differing by 15 per cent and values of— dp/dd differing by
only 3 per cent.
X. CONCLUSIONS
The vapor pressure of liquid and solid carbon dioxide has beenmeasured at this bureau in the range 31° to —79° C. The averagedeviation of the weighted observations from values calculated froman equation is 1.0 part in 10,000 for the liquid and 2.4 parts in 10,000for the solid. These average deviations correspond to about 0.004° C.for both liquid and solid. The value of the vapor pressure at 0° C.calculated from the equation for the liquid is only 1 part in 10,000less than that observed by O. C. Bridgeman.The measurements near the normal sublimation point (
— 78.514°
C.) are in agreement with those at the Reichsanstalt. The equationfor the solid has been designed to represent also the measurementsat temperatures below —79° C. by Henning and Stock, Siemens, andOnnes and Weber.The values of vapor pressure given in the Appendix to this paper
are considered accurate within 1 or 2 parts in 10,000 in the range 31°
to -80° C, 1 part in 1,000 in the range -80° to - 100° C, 1 per centin the range — 100° to — 140° C, and about 20 per cent in the range-140° to -190°C.The triple point pressure and temperature are 3,885.2 ±0.4 mm
and -56,602 ±0.005° C, respectively.
The critical point temperature is considered to be between 30.95°
and 31.05° C. For practical purposes the temperature may beassumed to be 31.00° C. for which the corresponding pressure is 73.76bars (72.80 atmospheres or 55,330 mm).
Observations of pressure and relative volumes along severalisotherms in the neighborhood of the critical point are given.The values of dp/dd in the Appendix obtained through differentia-
tion of the vapor pressure equations for the liquid and the solids areconsidered accurate within 1 part in 1,000 in the range 25° to — 100°
C, and within about 0.5 per cent near the critical point. The differ-
entiation of the vapor pressure equation for the solid leads to results
which together with volumetric data from other laboratories makepossible, through the Clapeyron-Clausius relation, a better estimateof latent heat of sublimation than has hitherto been made from suchdata. Such estimate is in agreement with the latent heat observedby Eucken and Donath. A graph (fig. 8) showing the relationbetween the latent heat and temperature is given. Values from thecurve BDE of this graph are considered to represent the latent heatof sublimation within 1 per cent down to liquid air temperatures andwithin 2 or 3 parts in 1,000 in the range -80° to -150° C.
408 Bureau of Standards Journal of Research [Vol. 10
XI. ACKNOWLEDGMENTSAcknowledgement is made to C. S. Taylor, who prepared and puri-
fied the carbon dioxide; to D. O. Burger for assistance in taking theobservations in 1931.
XII. APPENDIXThe values in the following tables have been calculated from equa-
tions (6) and (9) given in the text or from their differential equations.The temperatures recorded have been corrected to the internationaltemperature scale. The term "bar" is used in accordance with theusage now internationally accepted; that is, to indicate a pressure of
1,000,000 dynes per square centimeter or 0.96784 normal atmospheres.The term microbar is used to indicate a pressure of one dyne persquare centimeter.
The error caused by linear interpolation between the pressure givenevery degree may be appreciable especially for the solid, but linear
interpolation between the logarithms of these pressures will rarely
introduce an error greater than a unit in the last decimal place givenin the tables.
Table 7.
—
Vapor pressure of solid carbon dioxide
[In lbs. per in. 2, reduced to g=32.1740 ft. per sec 2
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